1. Technical Field
The present invention pertains to the field of cellular communication. More particularly, the present invention pertains to wireless communication of data as opposed to voice communication.
2. Discussion of Related Art
The invention concerns automatic retransmission request (ARQ) protocols for orthogonal frequency and code division multiplexing (OFCDM). The invention is a generalization of the so-called space-time adaptive retransmission (STAR) method, described e.g. in “Matrix modulation and adaptive retransmission,” by A. Hottinen and O. Tirkkonen, in Proc. IEEE ISSPA, July 2003, vol. 1, pp. 221-224. Accordingly, the invention is sometimes called Adaptive Retransmission for Frequency Spreading (ARFS).
An OFCDM signal model is as follows, in terms of baseband signals after FFT, assuming that the delay spread is smaller than the cyclic prefix, so that individual subcarriers experience frequency flat fading. Let us assume Walsh-Hadamard (WH) spreading with spreading factor S. This means that each symbol is spread over S subcarriers. Advantageously the subcarriers are interleaved, so that no subcarriers conveying a symbol are neighbors. Preferably, in the interleaving all groups of subcarriers belonging to the same spreading code are such that the distance (in frequency) between the subcarriers is as large as possible, and at a minimum, larger than a typical coherence bandwidth. Then the subcarriers over which a symbol are spread are likely to have uncorrelated or only weakly correlated channels. Also, we make the crucial assumption that in a downlink transmission at least some multicodes are transmitted to a single user. In an uplink transmission this reduces to requiring that multicode transmission is used on at least some of the spread subcarriers. In the HS-PDSCH (high speed-physical downlink shared channel), the capacity is shared primarily by time-division, but it is also possible to code multiplex a few terminals (one to four) during the TTI. The channelization codes are allocated at a fixed spreading factor (16), but the base station may assign multiple channelization codes for one terminal during a TTI thus applying multicode transmission.
Preferably, WH-spreading codes are not used to separate users. Users may be separated in time or frequency. Because of separating a user preferably not by use of a spreading code, but instead by use of time or frequency separation, the term OFCDM is used here, instead of multi-carrier CDMA (MC-CDMA). (Typically MC-CDMA is also understood as a code-division method to separate users. Here we want to stress the “multi-code” aspect of MC-CDMA, and consider the situation where many codes in overlapping dimensions are allocated to the same user. That is why we use the terminology OFCDMA instead of MC-CDMA. There is though no reason not to use the term MC-CDMA as descriptive in the case that the spreading factor is smaller than the number of subcarriers, and preferably multicodes are allocated to users from the set of codes spreading over the same subcarriers.)
For a single transmit antenna at the transmitter and a single receive antenna at the receiver, the signal model would bey=HCx+n≡x+noise  (1)where y is an S×1 vector of received signals on the S subcarriers, H is an S×S diagonal matrix with the kth diagonal element representing the channel received on the kth subcarrier covered by the spreading code, C is an S×S spreading code matrix, each column being one spreading code, x is an S×1 vector of data transmitted on each spreading code,  is an S×S equivalent channel matrix, and n is additive noise.
Take for example the case of WH spreading using a spreading factor S=2. The signal model in this case can be written explicitly as:
                              [                                                                      y                  1                                                                                                      y                  2                                                              ]                =                                                                                                  1                                          2                                                        ⁡                                      [                                                                                                                        h                            1                                                                                                    0                                                                                                                      0                                                                                                      h                            2                                                                                                                ]                                                  ⁡                                  [                                                                                    1                                                                    1                                                                                                            1                                                                                              -                          1                                                                                                      ]                                            ⁡                              [                                                                                                    x                        1                                                                                                                                                x                        2                                                                                            ]                                      +            n                    =                                                                      1                                      2                                                  ⁡                                  [                                                                                                              h                          1                                                                                            0                                                                                                            0                                                                                              h                          2                                                                                                      ]                                            ⁡                              [                                                                                                                              x                          1                                                +                                                  x                          2                                                                                                                                                                                                  x                          1                                                -                                                  x                          2                                                                                                                    ]                                      +            n                                                            =                                                                      1                                      2                                                  ⁡                                  [                                                                                                              h                          1                                                                                                                      h                          1                                                                                                                                                              h                          2                                                                                                                      -                                                      h                            2                                                                                                                                ]                                            ⁡                              [                                                                                                    x                        1                                                                                                                                                x                        2                                                                                            ]                                      +            n                          ,            where hs is the channel on subcarrier s and represents the power of the subcarrier s, the WH spreading codes are normalized by the factor 1/√{square root over (2)}, and the matrix
  C  =      [                            1                          1                                      1                                      -            1                                ]  is the spreading code matrix and is made up of the two spreading codes (columns of the matrix)
         [                            1                                      1                      ]  and
               [                                    1                                                              -              1                                          ]        .  Thus,
  ℋ  =            1              2              ⁡          [                                                  h              1                                                          h              1                                                                          h              2                                                          -                              h                2                                                        ]      is the equivalent channel matrix for S=2.
It is straight forward to see that despite the spreading codes being orthogonal at transmission, the received signal is not orthogonal. The correlation matrix R of the transmitted signal is the so-called Gram matrix of the equivalent channel, i.e.
  R  =                    ℋ        †            ⁢      ℋ        =                            1          2                ⁡                  [                                                                                                                                                              h                        1                                                                                    2                                    +                                                                                                          h                        2                                                                                    2                                                                                                                                                                                        h                        1                                                                                    2                                    -                                                                                                          h                        2                                                                                    2                                                                                                                                                                                                                h                        1                                                                                    2                                    -                                                                                                          h                        2                                                                                    2                                                                                                                                                                                        h                        1                                                                                    2                                    +                                                                                                          h                        2                                                                                    2                                                                                ]                    =                        1          2                ⁡                  [                                                    a                                                              b                  pm                                                                                                      b                  pm                                                            a                                              ]                    where a is the total power of the subcarriers, i.e.
  a  =            ∑              s        =        1            S        ⁢                                    h          2                            2      and bpm is the interference between the code channels, given by:bpm=|h1|2−|h2|2.The interference vanishes and the received signal is orthogonal only if |h1|2=|h2|2, which would occur for frequency flat fading.
The simplest receiver is a matched filter receiver, indicated by † yielding output:z=†y.Written in terms of the transmitted signal and noise, the matched filter output isz=Rx+†n. If the matched filter is judged to be a sufficient receiver, symbol estimates are directly constructed from z=†y. More reliable estimates may be constructed by attempting to invert the dependence of the correlation matrix in z=Rx+†n. Thus e.g a zero-forcing (de-correlating) receiver applies the pseudo-inverse on the received signal,{circumflex over (x)}=R−1†y=x+R−1†n. The resulting symbol estimates are corrupted by colored noise. A Linear Minimum Mean Square Error estimate (LMMSE) is constructed using the pseudo-inverse with a noise estimate added to R in the inverse. (The effects of the colored noise can be mitigated by applying even more complicated detectors of the M-algorithm type, preferably based on a so-called QR-decomposition.)
In conventional ARQ, the retransmissions are exactly similar to the first transmission. If hard decision demodulation is used, the matched filtering is performed exactly as for the first transmission. After that, the matched filter outputs are summed, as well as the correlation matrices (or pseudo inverses), and the de-correlating, LMMSE or non-linear demodulation algorithm is used. For S=2, the correlation matrix for a second transmission according to conventional ARQ is:
      R    ~    =            1      2        ⁡          [                                                  a              ~                                                                          b                ~                            pm                                                                                          b                ~                            pm                                                          a              ~                                          ]      where ã and {tilde over (b)}pm are the total channel power and correlation coefficients, with hs replaced by the channel {tilde over (h)}s during the retransmission. The sum of the original matched filter output and the matched filter output for the retransmission is:z+{tilde over (z)}=(R+{tilde over (R)})x+†n+† nwhere the sum of the correlation matrices is:
            R      +              R        ~              =                  1        2            ⁡              [                                                            a                +                                  a                  ~                                                                                                      b                  pm                                +                                                      b                    ~                                    pm                                                                                                                          b                  pm                                +                                                      b                    ~                                    pm                                                                                    a                +                                  a                  ~                                                                    ]              ,which shows the diversity advantage if the retransmission is outside the channel coherence time. The channel powers add coherently, whereas the self-interference terms add non-coherently (as real numbers). Thus the expected relative self-interference after a retransmission is smaller than before. If, however, the retransmission is within the channel coherence time, the sum correlation is just twice that for R Both channel power and self-interference add coherently. The only gain from the retransmission is that noise combines non-coherently, so the signal to interference and noise ratio (SINR) is improved.
Thus, with conventional ARQ, the complexity of detecting two transmissions is exactly twice the complexity of receiving one transmission, plus the complexity of summing the two matched filter outputs and correlation matrices/pseudo inverses. For soft output demodulation, the procedure described above may be followed with a step of combining the transmissions. Alternatively, soft outputs may be constructed from the first and second transmission separately, and the likelihood ratios may be added. The overall complexity is approximately the same.
What is needed is needed is a way to perform retransmission without adding appreciably to the complexity of the receiver processing.